There is a light at the front of a circular arena. A boy starting from B
runs at the rate of 3 m/s toward the center C. At what rate will his
shadow be moving along the rear wall when he is halfway from B to C?

In your FAQ on circle formulas, in the sections where the other five
values are derived from any two known values, could you write each
formula in terms of only the two known values, instead of using the
intermediate steps?

A student of trigonometric identities seeks help with a proof involving sines of double and
quadruple angles, as well as a square root. Invoking de Moivre's Theorem to approach the
problem indirectly, Doctor Anthony manufactures a quadratic substitution with
particularly helpful root sums and products.

I am a tenth grade student taking AMF (advanced mathematical functions)
and was given the problem: 0<=X<=150; when does the Sin 8X = Sin X? I had
no problem doing this on my graphing calculator, and finding the
intersects between the functions, but is there any way to do this by
using some sort of equation?

Taught to evaluate trigonometric expressions with a calculator, a student wonders if
there are simple formulas behind sine, cosine, and tangent. Doctor Jerry introduces the Maclaurin series and CORDIC algorithm.